When a triangle $\Delta UVW$ is dilated from a point (in this case, point $U$) by a scale factor, all of its side lengths are scaled by that factor. If the scale factor is 2, this means that each side length of the triangle will be doubled.

Given that $\Delta UVW$ is dilated from point $U$ by a scale factor of 2, let's analyze the relationship between the original triangle and its image.

1. Original Triangle:

   • Let's denote the side lengths of the original triangle as $UV$, $UW$, and $VW$.

2. Dilated Triangle:

   • After dilation, the side lengths will become $U'V' = 2 \times UV$, $U'W' = 2 \times UW$, and $V'W' = 2 \times VW$.

Since all sides are scaled by a factor of 2, the ratios of corresponding sides between the original and the dilated triangles will be equal:

$\frac{U'V'}{UV} = \frac{U'W'}{UW} = \frac{V'W'}{VW} = 2$

This equality tells us that all sides in the image are twice as long as the corresponding sides in the original triangle.

Conclusion

The true statement regarding the dilation is: $\frac{U'V'}{UV} = \frac{U'W'}{UW} = \frac{V'W'}{VW} = 2$

If this equation matches one of the choices provided (though the options are not listed explicitly), it is the correct choice.

Do you have any questions, or would you like more details on any of these points?

Related Questions

1. What happens if the scale factor for dilation is less than 1?
2. How does dilation affect the angles of a triangle?
3. Can dilation be performed from a point outside of the triangle?
4. How do you find the coordinates of a dilated triangle in the coordinate plane?
5. What is the difference between dilation and reflection in geometry?

Tip

When working with dilations, always remember that all distances from the center of dilation (point $U$ in this case) will change proportionally to the scale factor.